The Atlas of
Knowledge and Ignorance

What humanity knows. What it doesn't. Where the frontier is.

3,000 open problems across every field of human inquiry — mathematics, sciences, and the humanities — mapped alongside the established results that define what we know. Not a textbook. A navigable map of the state of play.

3,000+
Open problems mapped
650+
Established results
300+
Fields covered
3
Reasoning tools
45
"Settled" problems that aren't

Two sides of the same map

Knowledge without ignorance is complacent. Ignorance without knowledge is lost.

🟢
Knowledge
The established results — theorems proved, mechanisms understood, frameworks that organize what we know. Each one earned, each one with a story. The floor we stand on.
354Established results
75New expansion results
3Domains (math · science · humanities)
🔵
Ignorance
The open problems — conjectures unresolved, mechanisms unknown, questions that define the frontier. Each one honest about what we don't yet know. The ceiling we push against.
3,000Open problems
303Mapped in the reasoning graph
160New expansion problems

Explore the Atlas

Each section is a self-contained interactive tool. Start anywhere.

The Map
Unified Atlas
The full map — 657 nodes (results and open problems) across all fields, with connections, hubs, and barriers. The single view of the state of knowledge.
657 nodes · 25 hubs
Open the map → Ignorance
3,000 Open Problems
1,000 in mathematics. 1,000 in the sciences. 1,000 in the humanities. Ten per field, across 300 fields. Every one genuinely open.
3,000 problems · 300 fields
Browse open problems → Knowledge
Established Results
The theorems, frameworks, and discoveries that define the floor of human knowledge — organized by domain, searchable, with significance and context.
354+ results across 3 domains
Browse results → Tool
Reasoning Engine
Set any claim true or false and watch consequences propagate through the graph. The "what if" tool — interventional, probabilistic, self-auditing.
706 claims · 154 edges · 20 conjunctions
Run the engine → Tool
Direction Finder
Three lenses over the reasoning graph: solve-together combos, best-supported frontiers, and cross-domain links. Shows where the map is dense and where it's thin.
Combos · Frontiers · Cross-domain
Find directions → Tool
Reduction Atlas
How fields reduce to each other — the structural skeleton of knowledge. Which results in one domain imply results in another.
See reductions → Unique
Contested as Settled
Problems widely treated as closed that aren't. The false negatives of human knowledge — reopened, pseudo-settled, pendulum, and zombie. Nothing else like this exists.
45 contested "settlements" · 4 status types
See what isn't settled → Expansion
Coverage Expansion
60 new domains closing gaps in social philosophy, non-Western thought, applied ethics, medicine, and CS. Contested fields mapped neutrally.
60 domains · 160 open · 75 results
Explore the expansion →

The verification failures you won't find anywhere else

"Contested as Settled" maps problems that textbooks, survey courses, and popular accounts file under solved — but aren't. Four distinct ways verification goes wrong:

Reopened
Consensus existed. New evidence cracked it.
Pseudo-settled
Closed in pedagogy. Live at the frontier.
Pendulum
Declared settled repeatedly, in alternating directions.
Zombie
Empirically dead. Still cited as alive.
See all 45 →

ELI5 Mode

Every entry has a plain-language version. Toggle ELI5 mode on any atlas page to swap technical descriptions for explanations anyone can follow. 775 explainers and counting.

775 ELI5s available